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Ronse, Christian

doi:10.1023/a:1008210216583

Cited by 91 publications

(10 citation statements)

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“…connections [29,30,14,31], hyperconnections [12], or directed connections [32]. The relations among various definitions of connections have been studied in [33].…”

Section: Related Work 50mentioning

confidence: 99%

Connected image processing with multivariate attributes: An unsupervised Markovian classification approach

Collet¹

2015

Computer Vision and Image Understanding

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This article presents a new approach for constructing connected operators for image processing and analysis. It relies on a hierarchical Markovian unsupervised algorithm in order to classify the nodes of the traditional Max-Tree. This approach enables to naturally handle multivariate attributes in a robust non-local way. The technique is demonstrated on several image analysis tasks: filtering, segmentation, and source detection, on astronomical and biomedical images. The obtained results show that the method is competitive despite its general formulation. This article provides also a new insight in the field of hierarchical Markovian image processing showing that morphological trees can advantageously replace traditional quadtrees.

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“…connections [29,30,14,31], hyperconnections [12], or directed connections [32]. The relations among various definitions of connections have been studied in [33].…”

Section: Related Work 50mentioning

confidence: 99%

Connected image processing with multivariate attributes: An unsupervised Markovian classification approach

Collet¹

2015

Computer Vision and Image Understanding

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“…Connectivity is an important issue in morphological image processing, it intervenes in image filtering and segmentation (Ronse and Serra, 2010;Salembier, 2010;Salembier and Wilkinson, 2009;Serra et al, 2010). The notion of a connected object was formalized by Serra (1988) who defined a connection on sets, for which alternate axioms were given in (Ronse, 1998). This concept was generalized by Ronse (2008) who introduced the notion of a partial connection.…”

Section: Introductionmentioning

confidence: 99%

“…These general axioms allowed to define new connectivities, for instance by clustering into a single connected component objects at a small distance from each other (Serra, 1988), or by restricting connectivity to objects having a minimum width (Ronse, 1998). Other examples of connections and partial connections can be found in (Ouzounis and Wilkinson, 2007;Ronse, 2008;Ronse and Serra, 2010).…”

Section: Introductionmentioning

confidence: 99%

“…Another limitation is that this approach restricts itself to the connectivity in directed graphs; it is an oriented version of graph connectivity. Following the unification of various connectivities under the more general concept of a connection (Serra, 1988;Ronse, 1998) or a partial connection (Ronse, 2008), we can similarly give general axioms for oriented connectivity: given an arbitrary space E, we consider a family of ordered pairs (p, S ) ∈ E × P(E) satisfying some general properties that are indeed satisfied in the special case of Tankyevych et al (2013). We will do this in Section 2, and this structure will be called a reach; it is characterized by three axioms called the union, transitivity and membership properties; a fourth point property deals with the connectivity of singletons (as in connections), and it leads to a full reach.…”

Section: Introductionmentioning

confidence: 99%

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Axiomatics for oriented connectivity

Ronse¹

2014

Pattern Recognition Letters

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Tankyevych et al. (2013) considered, in a directed graph, any set S of vertices where there is some marker vertex p ∈ S such that for every vertex x ∈ S , there is a directed path from p to x included in S ; the family of all such sets S was called a semi-connection. Their properties were briefly analysed and compared with connectivity and connected components in undirected graphs.We give an abstract algebraic formalization of this concept, following the same approach as that of Serra (1988) and Ronse ( 2008) for the notions of connection and partial connection, which generalize both topological and graph-theoretic connectivity.Here the sets S are unsufficient, one must associate to them their markers p; thus in a space E we consider a family R of ordered pairs (p, S ) ∈ E × P(E), where the set S can be "reached" from marker p; this family, which we call a reach, must satisfy the three properties of union, transitivity and membership; a fourth point property leads to a full reach. As in (Serra, 1988;Ronse, 2008), we give an equivalent definition in terms of a system of point openings (γ p , p ∈ E) satisfying some properties. The special case of symmetry, where S does not depend on the choice of the marker p ∈ S , leads to a partial connection or a connection. Some examples are given.Possible applications of this new theory lie in the analysis of connected structures having an orientation, for instance vascular networks in medical imaging. One can also apply it to geodesic reconstruction and connected filtering.

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“…Connectivity-based image segmentation [8] is then applied to automatically identify liquid spray structures. Distinct regions smaller than a stable droplet-size threshold [9] are identified as individual droplets.…”

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confidence: 99%